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SashulF [63]
3 years ago
10

Heya!

Mathematics
2 answers:
dimulka [17.4K]3 years ago
6 0

Answer:

the answer is in last picture

ArbitrLikvidat [17]3 years ago
4 0

Answer:

See Below.

Step-by-step explanation:

We are given that PQRS is a square. A, B, C, and D are the points of the sides PQ, QR, RS, and SP, respectively.

And we are given that AQ = BR = CS = DP.

This is shown in the figure below.

And we want to prove that ABCD is a square.

Since PQRS is a square, it follows that:

m\angle P=m\angle Q=m\angle R=m\angle S=90^\circ

Likewise:

PQ=QR=RS=SP

PQ is the sum of the segments PA and AQ:

PQ=PA+AQ

Likewise, QR is the sum of the segments QB and BR:

QR=QB+BR

Since AQ = BR and PQ = QR:

PA+AQ=QB+AQ

Therefore:

PA=QB

Likewise, RS is the sum of the segments RC and CS:

RS=RC+CS

Since RS = PQ and CS = AQ:

RC+CS=PA+CS

Thus:

RC=PA=QB

Repeating this procedure for the remaining side, we acquire that:

PA=QB=RC=SD

And since each of the angles ∠P, ∠Q, ∠R, and ∠S is 90°, by the SAS Theorem, we acquire:

\Delta AQB\cong\Delta BRC\cong \Delta CSD\cong \Delta DPA

Then by CPCTC, we acquire:

AB=BC=CD=DA

However, this means that ABCD could be either a rhombus or a square, so we need to prove that the angles are right angles.

The interior angles of a triangle always sum to 180°. Since they are right triangles, the two other angles must equal 90°. Thus, for ΔAQB:

m\angle QAB+m\angle QBA=90^\circ

By CPCTC, ∠PAD≅∠QBA. Thus:

m\angle QAB+m\angle PAD=90^\circ

∠DAB forms a linear pair. Therefore:

m\angle PAD+m\angle QAB+m\angle DAB=180

By substitution and simplification:

m\angle DAB=90^\circ

So, ∠DAB is a right angle.

By repeating this procedure, we can establish that ∠ABC, ∠BCD, and ∠CDA are all right angles. This is not necessary, however. Since we concluded that AB = BC = CD = DA, and that we have one right angle, then ABCD must be a square.

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Which number is rational?
irina [24]
D
hope this helps
this is because the .3 is repeating but it is the same number repeating(it is a pattern)
3 0
4 years ago
Help me i dont really understand
xenn [34]

Answer:

73

Step-by-step explanation:

12(6) + 1/4 • 2^2

Square the 2 first.

12(6) + 1/4 • 4

Then multiply from left to right.

72 + 1

Lastly, add.

73

The parenthesis around the 6 mean multiplication, not the Parenthesis that are grouping symbols if you are learning PEMDAS. So your question has no grouping symbol parenthesis. Next comes Exponents, that's why we squared the 2. Multiply and Divide come next IN THE ORDER THAT THEY APPEAR FROM LEFT TO RIGHT. Then the same method with adding and subtracting. That's called the order of operations.

3 0
2 years ago
If a = 7 and b = 11, what is the measure of ∠B? (round to the nearest tenth of a degree) A) 32.5° B) 39.2° C) 50.5° D) 57.5°
Ilia_Sergeevich [38]

Answer:

D) 57.5°

Step-by-step explanation:

As the question is not complete. So, let's suppose it is a right angle triangle then, we can apply Pythagoras theorem to calculate the hypotenuse or the third side.

Pythagoras Theorem = c^{2} = a^{2} + b^{2}

a = 7 and b = 11

a^{2} = 49

b^{2} = 121

Plugging in the values, we will get:

c^{2} = 49 + 121

c^{2} = 170

c = \sqrt{170}

To calculate the unknown angle B, we can use law of sine.

Law of sine = \frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}

So,

\frac{c}{sinC} = \frac{b}{sinB}

\frac{\sqrt{170} }{sin90} =  \frac{11}{sinB}

Sin90 = 1

sinB = \frac{11}{\sqrt{170} }

B = sin^{-1} (\frac{11}{\sqrt{170} })

B = 57.5°

8 0
3 years ago
In JKL. solve for x <br><br> 66.73<br> 74.89<br> 15.44<br> 38.16
liq [111]
By right triangle trigonometry, the sine of the measure of an angle is the ratio of the opposite side of this angle to the hypotenuse.

Thus, \displaystyle{\sin27^{\circ}= \frac{34}{x}


\sin27^{\circ} is a constant which can be found using a calculator:

with calc in pc: view → scientific → 27→sin = 0.45399, 

thus x=34/0.45399=74.89


Answer: 74.89
5 0
3 years ago
Help pls! First to answer gets brainliest
amid [387]
Answer: $3.92
STEOS TO SOLUTION: take $19.62 and divide by 5
7 0
3 years ago
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